Networks with condorcet solutions

A Condorcet point on a network is a point such that thare is no other point closer to a strict majority of users which are located at the vertices of the network. A complete characterization is given of those networks on which no Condorcet paradox occurs, in the sense that for each distribution of users there exists at least one Condorcet point. Moreover, those networks are characterized on which Condorcet points and Weber points always coincide. A polynomial algorithm is obtained which decides whether a given network has Condorcet points for all distributions of users on the network.     

Indecomposables with smaller cohomological length in the derived category of gentle algebras Dedicated to Professor Yingbo Zhang on the Occasion of Her 70th Birthday

Bongartz(2013) and Ringel(2011) proved that there is no gaps in the sequence of lengths of indecomposable modules for the ?nite-dimensional algebras over algebraically closed ?elds. The present paper mainly studies this "no gaps" theorem as to cohomological length for the bounded derived category Db(A) of a gentle algebra A: if there is an indecomposable object in D~b(A) of cohomological length l 1, then there exists an indecomposable with cohomological length l-1.     

关于4阶极小渐近基的一个结果

设h≥2,若h阶渐近基A的任一真子集均不是h阶渐近基,则称集合A是自然数集N的h阶极小渐近基.为进一步刻画渐近基与极小渐近基之间的关系,本文综合运用自然数的b进制表示理论及分类讨论的方法,证明了存在一个集合是4阶渐近基且其任何子集均不是4阶极小渐近基.     

Minimal transformations with no common factor need not be disjoint

A countable family of minimal transformations (X, Z) is described for which no pair have a non-trivial common factor, and so that no pair is disjoint. This answers in the negative a question of H. Furstenberg.     

Families of fixed-point cellular rotations

A cellular rotation is a pseudofree cellular automorphism, with no non-fixed pseudofixed points, of a graph embedded in an orientable surface. A family of cellular rotations is a collection of cellular rotations having one embedding of each genus above some fixed minimum genus, all sharing the same quotient embedding and, in an appropriate sense, the same voltage-assignment data. We provide a complete catalog of all families of cellular rotations having at least one fixed point, and provide preliminary results regarding families of cellular rotations having no fixed points.     

最大利润流问题及算法

最大利润流是以运输利润最大为目标的网络优化问题 .一个利润可行流可分解为若干个路流和圈流 ,相应地该可行流的利润也等于这些路流和圈流的利润之和 .本文证明了一个可行流为最大利润流的充要条件是不存在利润增广路 ,并据此提出了求解算法 .文章最后给出了一个计算实例 .     

Quasi-minimal enumeration degrees and minimal Turing degrees

We show that there exists a set A such that A has quasi-minimal enumeration degree, and there are uncountably many sets B such that A is enumeration reducible to B and B has minimal Turing degree. Answering a related question raised by Solon, we also show that there exists a nontotal enumeration degree which is not e-hyperimmune.During the preparation of this paper, Slaman was partially supported by the HCM European Program no. ERBCHRXCT930415 (while he was visiting the University of Leeds), by NSF Grant DMS-9500878 and was a CNR Visiting Professor at the University of Siena.The preparation of this paper was partially supported by the HCM European Program no. ERBCHRXCT930415 and by MURST 60%.     

Note on prime representations of convex polyhedral sets

Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant Nos. A8807, A4625, and A7742.     

Einstein solvmanifolds attached to two-step nilradicals

A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra which can serve as the nilradical of an Einstein metric solvable Lie algebra is called an Einstein nilradical. We give a classification of two-step nilpotent Einstein nilradicals with two-dimensional center. Informally, the defining matrix pencil must have no nilpotent blocks in the canonical form and no elementary divisors of a very high multiplicity. We also show that the dual to a two-step Einstein nilradical is not in general an Einstein nilradical.     

无爪3 -正则图的独立数

如果图G的一个集合X中任两个点不相邻, 则称 X 为独立集合. 如果 N[X]=V(G), 则称X是一个控制集合. i(G)(β(G))分别表示所有极大独立集合的最小(最大)基数. γ(G)(Γ(G))表示所有极小控制集合的最小(最大)基数. 在这篇论文中, 作者证明如下结论: (1) 如果 G ∈R 且G 是n阶3 -正则图, 则 γ(G)= i(G), β(G)=n/3. (2) 每个n阶连通无爪3 -正则图 G, 如果 G(G≠ K₄) 且不含诱导子图K₄-e, 则 β(G) =n/3.     

The proportional solution for rights problems

Recently there have been several studies to provide axiomatic characterizations of solutions to rights problems. However, these studies do not give a satisfactory answer to the question why the proportional solution is the most widely used. This is the question addressed in this paper. To that purpose, we adopt the axiomatic approach; we suggest a set of axioms which a desirable solution should satisfy and we show that the proportional solution is the only solution to satisfy these axioms. Our main axioms are no advantageous reallocation and additivity. A solution satisfies no advantageous reallocation if no subgroup of claimants ever benefits by transferring parts of their claims between themselves. A solution satisfies additivity if it yields the same allocation whether the total estate is divided at once or in several steps.     

Measurable solutions for stochastic evolution equations without uniqueness

A method for obtaining measurable solutions to stochastic evolution equations in which there is no uniqueness for the corresponding non-stochastic equation is presented. It involves a technique based on a measurable selection theorem for set-valued functions. No assumptions are needed on the underlying probability space. An application is given to the stochastic Navier–Stokes problem in arbitrary dimensions. We also show the existence of measurable solutions to stochastic ordinary differential equations in which there is no uniqueness. A finite-dimensional generalization is given to adapted solutions in the case of a normal filtration and path uniqueness.     

Elusive groups of automorphisms of digraphs of small valency

A transitive permutation group is called elusive if it contains no semiregular element. We show that no group of automorphisms of a connected graph of valency at most four is elusive and determine all the elusive groups of automorphisms of connected digraphs of out-valency at most three.     

一个代数的预投射分支和τ-预投射分支

设A是一个Artin代数,Γ_A是A的Auslander-Reiten箭图。我们得到:如果Γ是Γ_A的一个不包含有向循环的预投射分支,那么Γ是Γ_A的一个τ-预投射分支,且对一个拟倾斜代数A,Γ是Γ_A的一个预投射分支当且仅当Γ是Γ_A的一个,τ-预投射分支。     

Exchange rings,units and idempotents

An associative ring R with identity is semiperfect if and only if every element of R is a sum of a unit and an idempotent, and R contains no infinite set of orthogonal idempotents. A ring which contains no infinite set of orthogonal idempotents is an exchange ring if and only if every element is a sum of a unit and an idempo-tent     

Maximum Order of Triangle‐Free Graphs with a Given Rank

The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle‐free graphs with a given rank and characterize all such graphs achieving the maximum order.     

Neighbor Sum Distinguishing Total Coloring of Triangle Free IC-planar Graphs

A graph is IC-planar if it admits a drawing in the plane such that each edge is crossed at most once and two crossed edges share no common end-vertex.A proper total-k-coloring of G is called neighbor sum distinguishing if∑_c(u)≠∑_c(v)for each edge uv∈E(G),where∑_c(v)denote the sum of the color of a vertex v and the colors of edges incident with v.The least number k needed for such a total coloring of G,denoted byχ∑"is the neighbor sum distinguishing total chromatic number.Pilsniak and Wozniak conjecturedχ∑"(G)≤Δ(G)+3 for any simple graph with maximum degreeΔ(G).By using the famous Combinatorial Nullstellensatz,we prove that above conjecture holds for any triangle free IC-planar graph with△(G)≥7.Moreover,it holds for any triangle free planar graph withΔ(G)≥6.     

Maximum order of trees and bipartite graphs with a given rank

The rank of a graph is that of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced trees as well as bipartite graphs with a given rank and characterize those graphs achieving the maximum order.     

Chebyshev solution of overdetermined systems of linear equations

A simplex algorithm for the Chebyshev solution of overdetermined systems of linear equations is described. In this algorithm, an initial basic feasible solution is available with no artificial variables needed. Also minimum storage is required and no conditions are imposed on the coefficient matrix. The algorithm is a simple and fast one. Numerical results are given.     

2－幂零代数与外导子

本文主要证明了以下定理：设Δ是有限连通箭图，A=kΔ/F²则Ａ到Ｄ（Ａ）的外导于为零的充要条件是Δ不含长度为２的圈．